In this paper we derive the eikonal method to directly approximate the
ratios of adjacent moments in the moment hierarchy. Our starting
point will be the generator
from [1]}, [2]}. The
steady-state condition will reduce to a set of stationary-path
equations that are the same as those for eikonals in Doi-Peliti
theory. The new feature resulting from the moment representation is a
mapping from the order \(k\)  of a moment to a specific position along
the particular escape trajectory that governs the ratio of that moment
to its local neighbors.
